This paper points out the influence of the internal flow of two-phase oil and gas mixtures on the motion of slender risers hanging from floating production units in curved configurations (for instance, catenary risers) used for offshore petroleum production in deep waters. The internal flow mass and momentum may impose a natural whipping displacement adding to the concerns of stress and fatigue. Usually, the internal flow may display different two-phase patterns (bubble, slug, churn, annular or stratified mixtures) possessing completely different characteristics; in the case of slugs, their intemittency may induce an oscillatory movement on the suspended pipeline. The fluid dynamic forces depend on the flow rates of both oil and gas phases, requiring the simulation of the pipeline movement under production conditions. In this paper, a modeling of induced forces caused by the internal two-phase slug flow is described, and results from numerical simulations are presented for a steel catenary riser configuration, showing the importance of the internal flow forces on the movements of a production riser.